Study on the Transient Temperature Field Based on the Fractional Heat Conduction Equation for Laser Heating

XU Guang-ying; WANG Jin-bao; HAN Zhi

doi:10.3879/j.issn.1000-0887.2015.08.006

Volume 36 Issue 8

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XU Guang-ying, WANG Jin-bao, HAN Zhi. Study on the Transient Temperature Field Based on the Fractional Heat Conduction Equation for Laser Heating[J]. Applied Mathematics and Mechanics, 2015, 36(8): 844-854. doi: 10.3879/j.issn.1000-0887.2015.08.006

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Study on the Transient Temperature Field Based on the Fractional Heat Conduction Equation for Laser Heating

doi: 10.3879/j.issn.1000-0887.2015.08.006

School of Maritime and Civil Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, P.R.China

Received Date: 2015-01-29
Rev Recd Date: 2015-04-22
Publish Date: 2015-08-15

Abstract

Abstract

Based on the fractional Taylor series expansion principle, the 1st-order fractional approximate heat conduction constitutive equation was formulated through expansion of the single-phase lag model. Combined with the energy equation, the fractional heat conduction equations were built for short pulse laser heating, and the Laplace transform was applied to solve the equations and obtain the analytical solution of the volumetric heat source temperature field of the non-Gauss time type. The properties of the temperature wave influenced by the fractional order were investigated based on specific examples. The thermal wave velocity decreases and its amplitude increases with the fractional order. The fractional heat conduction equation is applicable for depicting the intermediate heat conduction process between that of the Fourier diffusion equation and that of the thermal wave equation. The correlation between the heat conduction mechanism and the fractional derivative terms in the fractional heat conduction equation was also fully discussed.
- fractional Cattaneo heat conduction,
- laser heating,
- fractional derivative,
- fractional Taylor’s formula

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References

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